A Tridimensional Hilbert-like Curve defined with {X1(...),Y1(...),Z1(...)} -iteration 1- [Une courbe tridimensionnelle du type Hilbert définie avec {X1(...),Y1(...),Z1(...)} -itération 1-].
A Tridimensional Hilbert-like Curve defined with {X1(...),Y1(...),Z1(...)} -iteration 1- [Une courbe tridimensionnelle du type Hilbert définie avec {X1(...),Y1(...),Z1(...)} -itération 1-].
defined by means of 3 real functions of T
(T ∈ [0,1])
X1(T) ∈ [0,1], Y1(T) ∈ [0,1] and Z1(T) ∈ [0,1]
such as
:
X1(T=0)=0 Y1(T=0)=0 Z1(T=0)=0 (lower left foreground corner)
X1(T=1)=1 Y1(T=1)=0 Z1(T=1)=0 (lower right foreground corner)
Ci(T) = {Xi(T),Yi(T),Zi(T)} ∈ [0,1]x[0,1]x[0,1] --> Ci+1(T) = {Xi+1(T),Yi+1(T),Zi+1(T)} ∈ [0,1]x[0,1]x[0,1]
if T ∈ [0,1/8[:
Xi+1(T) = Xi(8T-0)
Yi+1(T) = Zi(8T-0)
Zi+1(T) = Yi(8T-0)
Transformation 1
if T ∈ [1/8,2/8[:
Xi+1(T) = Zi(8T-1)
Yi+1(T) = 1+Yi(8T-1)
Zi+1(T) = Xi(8T-1)
Transformation 2
if T ∈ [2/8,3/8[:
Xi+1(T) = 1+Xi(8T-2)
Yi+1(T) = 1+Yi(8T-2)
Zi+1(T) = Zi(8T-2)
Transformation 3
if T ∈ [3/8,4/8[:
Xi+1(T) = 1+Zi(8T-3)
Yi+1(T) = 1-Xi(8T-3)
Zi+1(T) = 1-Yi(8T-3)
Transformation 4
if T ∈ [4/8,5/8[:
Xi+1(T) = 2-Zi(8T-4)
Yi+1(T) = 1-Xi(8T-4)
Zi+1(T) = 1+Yi(8T-4)
Transformation 5
if T ∈ [5/8,6/8[:
Xi+1(T) = 1+Xi(8T-5)
Yi+1(T) = 1+Yi(8T-5)
Zi+1(T) = 1+Zi(8T-5)
Transformation 6
if T ∈ [6/8,7/8[:
Xi+1(T) = 1-Zi(8T-6)
Yi+1(T) = 1+Yi(8T-6)
Zi+1(T) = 2-Xi(8T-6)
Transformation 7
if T ∈ [7/8,1]:
Xi+1(T) = Xi(8T-7)
Yi+1(T) = 1-Zi(8T-7)
Zi+1(T) = 2-Yi(8T-7)
Transformation 8
[See the used color set to display the parameter T]
